Human immunodeficiency virus (HIV) is a virus that destroys the body's immune system. People infected with HIV can sometimes develop problems with memory, thinking and concentration. Individuals are invited to participate in this study testing the effect of CPI-1189 because they have HIV-related memory, thinking, concentration and motor problems. Antiretroviral agents are the only proven therapy for treating HIV thinking problems, but the treatment response is often poor. One reason for this poor response to antiretroviral agents may be that brain inflammation may be contributing to the dementia in addition to the brain virus infection. CPI-1189 is an experimental drug which may decrease inflammation in the brain. The trial will compare CPI-1189 to a placebo (an inactive substance similar to a sugar pill). This research study will examine how well people with HIV infection tolerate CPI-1189 and how safe this medicine is. The study will also see if there is any benefit of this drug on memory, thinking and concentration problems.